The Dunkl-Coulomb problem in the plane

  title={The Dunkl-Coulomb problem in the plane},
  author={Vincent X. Genest and A. Lapointe and L. Vinet},
  journal={arXiv: Mathematical Physics},
The Dunkl-Coulomb system in the plane is considered. The model is defined in terms of the Dunkl Laplacian, which involves reflection operators, with a $r^{-1}$ potential. The system is shown to be maximally superintegrable and exactly solvable. The spectrum of the Hamiltonian is derived algebraically using a realization of $\mathfrak{so}(2,1)$ in terms of Dunkl operators. The symmetry operators generalizing the Runge-Lenz vector are constructed. On eigenspaces of fixed energy, the invariance… Expand
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